Question

Find equation of a line parallel given point. Write the equation in slope-intercept form Line 3x+4y=12, point (0,4)

Answer 1

Given:

`\begin{gathered} Li\text{ne 1;} \\ 3x+4y=12 \\ \text{Point (0,4)} \end{gathered}`

To get the equation of the second line, it has the same slope as Line 1 because the two lines are parallel.

Hence, the slope

`m_1=m_2`

`\begin{gathered} 3x+4y=12 \\ In\text{ slope-intercept form,} \\ y=mx+b \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \\ \\ \text{Thus;} \\ 3x+4y=12 \\ 4y=-3x+12 \\ \text{Dividing all through by 4,} \\ y=-(3)/(4)x+(12)/(4) \\ y=-(3)/(4)x+3 \\ \\ \text{Hence,} \\ m_1=-(3)/(4) \end{gathered}`

To get the equation of the second line parallel to line 1, then;

`\begin{gathered} m_1=m_2 \\ \text{Thus,} \\ m_2=-(3)/(4) \end{gathered}`

The equation of the second line is gotten by the formula;

`\begin{gathered} (y-y_1)/(x-x_1)=m \\ \text{where;} \\ x_1=0 \\ y_1=4 \\ m=-(3)/(4) \end{gathered}`

Thus;

`\begin{gathered} (y-y_1)/(x-x_1)=m \\ (y-4)/(x-0)=-(3)/(4) \\ (y-4)/(x)=-(3)/(4) \\ \text{Cross multiplying;} \\ 4(y-4)=-3x \\ 4y-16=-3x \\ 4y=-3x+16 \\ \text{Dividing both sides all through by 4 to get the equation in slope-intercept form;} \\ y=-(3)/(4)x+(16)/(4) \\ y=-(3)/(4)x+4 \end{gathered}`

Therefore, in slope-intercept form, the equation of the line parallel to 3x + 4y = 12 through the point (0,4) is;

`y=-(3)/(4)x+4`